Composite binary endpoints are increasingly used as primary endpoints in clinical trials. When designing a trial, it is crucial to determine the appropriate sample size for testing the statistical differences between treatment groups for the primary endpoint. As shown in this work, when using a composite binary endpoint to size a trial, one needs to specify the event rates and the effect sizes of the composite components as well as the correlation between them. In practice, the marginal parameters of the components can be obtained from previous studies or pilot trials; however, the correlation is often not previously reported and thus usually unknown. We first show that the sample size for composite binary endpoints is strongly dependent on the correlation and, second, that slight deviations in the prior information on the marginal parameters may result in underpowered trials for achieving the study objectives at a pre-specified significance level. We propose a general strategy for calculating the required sample size when the correlation is not specified and accounting for uncertainty in the marginal parameter values. We present the web platform CompARE to characterize composite endpoints and to calculate the sample size just as we propose in this paper. We evaluate the performance of the proposal with a simulation study and illustrate it by means of a real case study using CompARE.